# Simplify ((3m^7)/(4y^5z^3))^4

(3m74y5z3)4
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 3m74y5z3.
(3m7)4(4y5z3)4
Apply the product rule to 3m7.
34(m7)4(4y5z3)4
Apply the product rule to 4y5z3.
34(m7)4(4y5)4(z3)4
Apply the product rule to 4y5.
34(m7)444(y5)4(z3)4
34(m7)444(y5)4(z3)4
Simplify the numerator.
Raise 3 to the power of 4.
81(m7)444(y5)4(z3)4
Multiply the exponents in (m7)4.
Apply the power rule and multiply exponents, (am)n=amn.
81m7⋅444(y5)4(z3)4
Multiply 7 by 4.
81m2844(y5)4(z3)4
81m2844(y5)4(z3)4
81m2844(y5)4(z3)4
Simplify the denominator.
Raise 4 to the power of 4.
81m28256(y5)4(z3)4
Multiply the exponents in (y5)4.
Apply the power rule and multiply exponents, (am)n=amn.
81m28256y5⋅4(z3)4
Multiply 5 by 4.
81m28256y20(z3)4
81m28256y20(z3)4
Multiply the exponents in (z3)4.
Apply the power rule and multiply exponents, (am)n=amn.
81m28256y20z3⋅4
Multiply 3 by 4.
81m28256y20z12
81m28256y20z12
81m28256y20z12
Simplify ((3m^7)/(4y^5z^3))^4

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